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### Lecture 09: Data Structure Transformations

Geography 128

Analytical and Computer Cartography

Spring 2007

Department of Geography

University of California, Santa Barbara

"In virtually all mapping applications it becomes necessary to convert from one cartographic data structure to another. The ability to perform these object-to-object transformations often is the single most critical determinant of a mapping system\'s flexibility" (Clarke, 1995)

Geocoding stamps coordinate system, resolution and projection onto objects

Data usually in generic formats at first

Can save space, gain flexibility, decrease processing time

Suit demands of analysis and modeling

Suit demands of map symbolization (e.g. fonts)

Why Transform Between Structures?Conversion of data collected at higher resolutions to lower resolution. Less data and less detail.

Simplicity -> clarity

Information will be lost

Generalization Transformations- Why Generalize?John Krygier and Denis Wood, Making Maps:

a visual guide to map design for GIS

Centroid

Map projections

Usually be seen as a part of Geocoding process

Generalization Transformations - Point-to-PointUSGS 1:250,000 3-arc second DEM format (1-degree block)

N-th Point retention

Equidistant re-sampling

Douglas-Peucker

Generalization Transformations - Line-to-Line GeneralizationDouglas-Peucker line generalization

Splines

Bezier Curves

Polynomial Functions

Trigonometric Functions (Fourier-based)

Generalization Transformations - Line-to-Line EnhancementProblem is given one set of regions, convert to another

Example: Convert census tract data to zip codes for marketing

Example: Convert crime data by police precinct to school district

May require dividing non-divisible measures, e.g population

Areal Interpolation

Greatest common geographic units: Full overlap set for reassignment

Generalization Transformations - Area-to-AreaPopulation at counties

Population at watersheds=?

Algorithm for Overlay

1. Intersections

2. Chain splitting

3. Polygon reassembly

4. Labeling and attribution

Generalization Transformations - Area-to-AreaCommon conversion between two major data structures, vector (TIN) and grid

Often via points and interpolation

Change cell size

Generate a new grid

Compute the intersect

Interpolate from neighboring cells

Problem of VIPs

Generalization Transformations Volume-to-Volumewww.soi.city.ac.uk/~jwo/phd/04param.php

Easy compared to inverse, a form of re-sampling

Grid must relate to coordinates (extent, bounds, resolution, orientation)

Rasters can be square, rectangular, hexagonal.

Resample at minimum r/2

Vector-to-Raster Transformations- Problem: What value goes into the cell?
- Dominant criterion
- Center-point criterion
- Separate arrays for dimensions and binary data?
- Index entries & look up tables

Convert form of vectors (e.g. to slope intercept)

Sample and convert to grid indices

Thin fat lines

Compute implicit inclusion (anti-alias)

Vector-to-Raster Transformations (cnt.)- Algorithmwww.inf.u-szeged.hu/~palagyi/skel/skel.html

Much harder, more error prone.

May involve cartographer intervention

Importance of alignment

Can do points, lines, area

Raster-to-Vector TransformationsSkeletonization and Thinning

Peeling

Expanding

Medial Axis

Feature Extraction

Topological Reconstruction

Raster-to-Vector Transformations- AlgorithmGrid Scan

Matrix Algebra - filtering

Raster-to-Vector Transformations- Edge Detectionfourier.eng.hmc.edu/.../gradient/node9.html

Scale transformations are lossy

(re)storage produce error

algorithmic error, systematic and random

Types are: scale, structural (data structure), dimensional, vector-to-raster

Data Structure TransformationsKate Beard: Source error, use error, process error

Morrison: Method-produced error

Error is inherent, can it be predicted, controlled or minimized?

XT = X\'

X\' T^-1 = X + E

The Role of Error- Errors are
- positional
- attribute
- systematic
- random
- known
- uncertain
- Errors can be attributed to poor choice of transformations
- Incompatible sequences of T\'s (non-invertible)
- "Hidden" Error=use error, not process error

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